A Variational Principle for Modeling Electronic Excitations in Gas and Condensed Phase

Accurate modeling of electronic excited states is one of the most important and challenging problems in electronic structure theory. This thesis focuses on a recently developed excited state variational principle and its applications in gas and condensed phase. In contrast to the widely used excited states method such as linear response (LR) and many-body perturbation theory (MBPT), which find excited states by perturbing around the ground state wave function or a zeroth order particle-hole excitation picture, the new excited state variational principle directly targets excited states with the full flexibility of an approximate wave function ansatz. Due to its non-perturbative nature, this method offers balanced and systematically improvable descriptions to excited states. We will also discuss the efficient implementation of the new excited state variational principle through variational Monte Carlo and the Linear Method optimization algorithm.The new excited state variational principle is applied to predict both the excitation energies of low lying excited states in small molecules and optical gaps in solids. In molecules, the new method yields order-of-magnitude of improvements over the state-of-art excited state methods based on LR theory in double excitations. In solids, not only is the new method demonstrated to be more accurate than the commonly used MBPT method, but it could also be used to analyze and provide insights into MBPT. In order to further extend the method’s applicability, we introduce a modified optimization method that addresses a fatal memory bottleneck in the original algorithm. With only minor lose in accuracy, the modified algorithm reduces the required memory per parallel process from tens of gigabytes to hundreds of megabytes. With the aid of the new optimization method, we show that the new excited state variational principle could systematically converge the excitation energy in a strongly correlated, Mott-insulating hydrogen ring with respect to increasing flexibility in the wave function ansatzes